During most current transmissions of radio, TV and data broadcasts conducted in particular through a cable or through terrestrial radio, data ise transmitted with a complex digital modulation method such as for example QAM (quadrature amplitude modulation). High-order symbol alphabets, for example according to 256-QAM or 1024-QAM, require a very precise adjustment of the reception in a reception device. In addition to Gaussian noise, the main problem is that a phase noise is created during the adjustment of the reception, which is produced by insufficient mixer and transmitter oscillators. Such phase noise causes statistical fluctuations in the system of coordinates of the received signal.
DE 103 44 756 A1 describes a circuit arrangement for symbol decision upon the reception of a signal coupled with a quadrature signal pair. The circuit arrangement is provided with a coordinate converter for conversion of the signal from Cartesian coordinates to non-Cartesian coordinates, a pre-decision device for determination of a minimal distance between a reception point and at least one corresponding nominal point based on the non-Cartesian signal, and a decision device for deciding a symbol based on the distance analysis. A control device in the circuit arrangement performs in this case a procedure for the determination of a symbol upon the reception of a signal which is coupled with a quadrature signal pair, during which the decision is made with an analysis of the distance of at least one reception point to at least one nominal point in the complex coordinate space. A particular characteristic in such a case is the fact that the distance in non-Cartesian or not exclusively Cartesian complex space is analyzed and a decision is then made based on this analysis. This makes it possible to avoid symbol decisions in a raster with boundaries which are optimized according to Gaussian noise. According to this procedure, decision cells are formed which in contrast to quadrants are widened in the phase direction, as one can see from the difference between FIG. 5 and FIG. 6.
FIG. 5 shows the first quadrant having 64[CCB1] QAM with possible symbols or symbol positions, symbol radii and Cartesian decision boundaries. FIG. 6, on the other hand, shows decision boundaries which are widened in the phase direction, as well as possible symbols and symbol radii.
This procedure makes it possible to ensure that a decision will be found not in the Cartesian space, that is to say in the system of I-Q coordinates, but in a system of polar coordinates. While with the Cartesian decision, a distance ΔI2+ΔQ2 between the digitalized input signal and an alphabet signal is minimized, with the decision in the system of polar coordinates is determined a distance a |Δr|+|Δφ, or the distance a Δr2+Δφ2, or a combination thereof.
Also possible is a combination of systems which takes into account both the parameters which are based on the system of polar coordinates and the parameters which are based on the Cartesian system. The factor a indicates in this case the form of the decision process and it can be adjusted according to reception conditions.
While according to the Cartesian decision, the boundaries are predetermined geometrically, in particular based on quadrant cells, and the decision can be easily realized by cutting off the low-order bits, all the distances must be explicitly calculated for the decision in the system of polar coordinates. To keep the expenditure required for this at a low level, preferably only probable symbols or symbol positions are included in the selection, for example only four possible symbols. An auxiliary decider is used for the selection according to the Cartesian decision type. A grid network of the auxiliary decider is illustrated in FIG. 7. Only four symbols in corner points of each quadrant of the auxiliary grid network are selected in order to make a decision, within which the received symbol is located. Other calculation rules are used for the outer regions.
The application of Viterbi decoders is generally known, and is used to correct an error of a trellis-coded information stream in which not all symbols are possible. In this case, after the reception of a sequence of symbols, the distance to several allowed symbols is compared and the most probable symbol sequence is selected, that is to say a symbol sequence which displays the lowest number of errors. The evaluation of the error is more precise when not only so called “hard” errors are taken into consideration, in which each false bit is evaluated as an error, but when also a “soft” error is considered within the framework of a so called soft decision.
Under the term soft error is referenced the distance which the received and digitalized signal had to the selected symbol, as well as the distance to the next most probable symbol.
The object of the present invention is to obtain an improved circuit arrangement and a method for deciding a symbol upon the reception of a signal which is coupled with a quadrature signal pair, provided with a procedure wherein the distance is analyzed in the non-Cartesian or not exclusively Cartesian complex coordinate space in order to obtain additional information about reliability.
This object is achieved with a method for deciding a symbol upon the reception of a signal coupled with a quadrature signal pair which has the characteristics according to embodiments described herein, and with a circuit arrangement for deciding a symbol upon the reception of a signal coupled with a quadrature signal pair having the characteristics according to embodiments describe herein.
A method for deciding a symbol upon the reception of a signal sd coupled with a quadrature signal pair is thus realized so that the decision is made with an analysis of the metric or of the distance of at least one reception point to at least one nominal point in a space of complex coordinates, and the metric in the non-exclusively Cartesian space of complex coordinates is analyzed and the decision is made on this basis, wherein the reliability of the decision is determined during the decision process.
The decision is preferably considered in a polar coordinate space, wherein for the metric, the Euclidean distance between the reception points and the nominal points is used, and/or a sum or the values of the angular projections and radial projections of the metric between the reception point and at least one nominal point are analyzed.
The reliability is preferably determined by taking into consideration the smallest metric between the reception point relative to both a first nominal point and to a second nominal point. The smallest metrics are in each case determined relative to nominal point for the previous symbol. The second nominal point forms preferably a second most probable point for the decision.
The reliability Z can be with advantage determined according to
  Z  =      log    (                            ∑                      A            ∈                          M              ⁢                                                          ⁢              1                                      ⁢                                  ⁢                  P          ⁡                      [                          s              =                              α                |                R                                      ]                                                ∑                      A            ∈                          M              ⁢                                                          ⁢              0                                      ⁢                                  ⁢                  P          ⁡                      [                          s              =                              α                |                R                                      ]                                )  with the sum of the conditional probability P[s=A|R] that the symbol α was transmitted if the symbol R was received formed over the set M1 of all transmission symbols which represent a sent value “1”, and the corresponding formation of sums over the set M0 of all transmission symbols which represent a “0”.
The reliability can be determined in a simple manner according to
  Z  =      log    ⁡          (                        P          ⁡                      [                          s              =                                                α                  ⁢                                                                          ⁢                  1                                |                R                                      ]                                    P          ⁡                      [                          s              =                                                α                  ⁢                                                                          ⁢                  0                                |                R                                      ]                              )      with p[s=α1|R] for the probability of a transmission symbol with the transmission value 1 and P[s=α0|R] for the probability of one of the most probable symbols having the transmission value 0.
The reliability Z can be in a particularly preferred version determined according toZ=abs[transmission](A1−A2)/NF=(A2−A1)/NF wherein A1 is the smallest metric for a most likely symbol position, A2 is second smallest metric for a second most probable symbol position, and NF is a normalization factor. The normalization factor is in this case preferably formed with the second smallest metric or the sum of the metrics or a constant.
Accordingly, preferred is a circuit arrangement for deciding a symbol upon the reception of a signal coupled with a quadrature signal part, provided with a coordinate converter for conversion of the signal from the Cartesian coordinates into non-Cartesian coordinates, and a decision device for deciding a symbol based on a distance analysis of a minimal metric between a reception point and two next most probable nominal points for this point, and a determination of the reliability of the decision. The circuit arrangement is used preferably in order to realize the method described above.
On the other hand, a decision that is per se known in a polar coordinate system is obtained with a corresponding decider or decision process at this time as a criterion for a soft decision[CB2]. In this manner, this new type of a decision is thus obtained with additional information for which the next Viterbi code is required.
Advantageous application fields can be found in complex digital modulation methods, such as for example QAM. Similar modulation methods are at this time employed in particular for radio, TV and data services which are transmitted via cable, but also through terrestrial radio.